\section{note of 2009.09.09}
\subsection{Time dependence of anomalous Green function}
In the normal Green function, where annihilator and creator paired, only relative time difference matter, the absolute time postilion does not matter and cancels out for a time-independent Hamiltonian.  The anomalous Green function has two annihilators or two creators, and the absolute time does bring in an extra phase factor.  (See \cite{Abrikosov}), they explicitly pull the factor $e^{\br{\mu_1+\mu_2}t}$ out.  

\subsection{Thought about Skip two 4-operator terms in the Motion of Equation of equal-time-pair wave-function }

In Zhang's thesis (\cite{ZhangThesis}), he omit two 4-operator terms with the argument that they introduce extra real coordinators and therefore introduce extra $\vk_F{}r_0$ terms, which is small in dilute system.  I am still a bit skeptical about whether it is appropriate in my problem. But it is probably OK.  We cannot make progress with some quite dangerous looking assumption, such throwing away all Hatree breaking of the four-operator term.

According to Zhang, the equation (Eq. 5.37) obtained by omit these two 4-operator terms still carries information about the many-body physics through the normalization of them.    


\subsection{}
$\chi_0$ in Zhang's thesis is not the two-body close-channel bound statfe, but should coincide it in the short length-scale except the normalization.  But then what?  Tony's suggestion is always to express everything back to the quantities measureable, such as $a_s$.  But it is unlikely only $a_s$ is enough.  What will be the other quantities that I can use?  

